In the previous chapter we have shown that is possible to obtain the gravitational potential between two compact objects from the Fourier transformation of a 4-point scattering amplitude.
On this chapter we want to use the multi-loop techniques introduced in chapterREF  and already applied in chapters REFREF , to evaluate 1-loop amplitudes which are necessary to compute post-Minkowskian corrections to physical processes. In the first part of this chapter, motivated by analogous studies done in other gauge theories such as QED or QCD [1]}, [2]}, we will be interested evaluation of 1-loop classical and quantum corrections to the process of light bending under a heavy object. Working in the effective field theory of General Relativity introduced in the previous chapter, we will study the scattering process of two scalar particles, one massive and one massless, up to one loop order. We will develop a computational algorithm in Mathematica to compute the 1-loop amplitude, and we will use it to obtain a prediction for the bending angle. We will confront our results with those appearing in literature [3]}, [4]}, [5]}, [6]}, finding extra pieces contributing to the quantum corrections to the bending angle, with respect to the known ones. Eventually, we will adapt this machinery to the evaluation of 1-loop amplitudes between two massive scalar particles, from which one can obtain the 1-loop corrections to the Newtonian potential.
